module Main where
 
import Prelude hiding ((+), (*), (^))
 
data N = Z | S N
  deriving (Eq, Show)
 
h :: N -> N -> N -> N
h       Z     _     b  = S b
h    (S Z)    a     Z  = a
h (S (S Z))   _     Z  = Z
h       _     _     Z  = S Z
h    (S n) (S a) (S b) = h n (S a) (h (S n) (S a) b)
 
(+) :: N -> N -> N
(+) = h (S Z)
 
(*) :: N -> N -> N
(*) = h (S (S Z))
 
(^) :: N -> N -> N
(^) = h (S (S (S Z)))
 
main = print ((S (S Z)) + (S (S (S Z)))) >>
       print ((S (S Z)) * (S (S (S Z)))) >>
       print ((S (S Z)) ^ (S (S (S Z))))

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